IB Physics Sub-topic E1 Notes

Nuclear radius

Remember that evidence for the nucleus was provided by the Rutherford-Geiger-Marsden experiment. During this, they found a clear relationship between a nucleus’s radius (R) and its atomic mass number (A). The equation is, where R₀ is the Fermi radius, equal to 1.20 x 10^-15 m:

$R = R_{0} A^{1/3}$

Additionally, at low energies, the intensity of α particles could be predicted from the angle of scattering, called Rutherford scattering. At high energies and low radii, however, this relationship disappeared.

So instead, nuclear scattering was performed with electrons. These do not feel the strong force and will instead diffract off nuclei. The wavelength of the fired electron can be calculated using the de Broglie formula:

$\lambda = \frac{hc}{E}$

Angular momentum

However, the Bohr model states that an electron does not emit energy when it is in a stable orbit. These are defined as orbits wherein the angular momentum (m_evr) of the orbit is a multiple (n) of h/2π. The equation for this is:

$m_{e}vr = \frac{nh}{2\pi}$

The energy of this orbit (E_n) is proportional to the inverse energy level². The formula for this is:

$E_{n}=-\frac{13.6eV}{n^2}$